SOLUTION: Use the center, vertices, and asymptotes to graph the hyperbola. (x - 1)^2 - 9(y

SOLUTION: Use the center, vertices, and asymptotes to graph the hyperbola. (x - 1)^2 - 9(y - 2)^2 = 9

Question 674921: Use the center, vertices, and asymptotes to graph the hyperbola.
(x - 1)^2 - 9(y - 2)^2 = 9
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Use the center, vertices, and asymptotes to graph the hyperbola.
(x - 1)^2 - 9(y - 2)^2 = 9
(x-1)^2/9 -(y-2)^2 = 1
This is a hyperbola with horizontal transverse axis.
Its standard form of equation:, (h,k)=coordinates of center
For given hyperbola:
center: (1,2)
a^2=9
a=3
vertices: (1�a,2)=(1�3,2)=(-2,2) and (4,2)
b^2=1
b=1
asymptotes are straight lines that go thru center and take the form: y=mx+b, m=slope, b=y-intercept
slopes of asymptotes for hyperbolas with horizontal transverse axis=�b/a=�1/3
..
equation of asymptote with negative slope:
y=-x/3+b
solve for b using coordinates of center
2=-1/3+b
b=7/3
equation: y=-x/3+7/3
...
equation of asymptote with positive slope:
y=x/3+b
solve for b using coordinates of center
2=1/3+b
b=5/3
equation: y=x/3+5/3
see graph below:
y=�(((x-1)^2-9)/9)^.5+2

RELATED QUESTIONS
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes? (answered by KMST)

Identify the center, vertices, foci, transverse, asymptotes, domain, and range for the... (answered by ewatrrr)

find the center, vertices, foci, and slopes of the asymptotes for each hyperbola whose... (answered by ewatrrr)

Find the center, vertices, and foci of the hyperbola. Graph the hyperbola.... (answered by ewatrrr)

Find the center, foci, vertices, and asymptotes of the hyperbola. x^2 - y^2 = 8(x-y)... (answered by ewatrrr)

For the following hyperbola: (x + 1)2 � (y � 3)2 = 1 (answered by lwsshak3)

Find the center, vertices, foci, and asymptotes of the hyperbola. {{{(x+4)^2/16 -... (answered by lwsshak3)

Sketch the hyperbolas. Identify the center, asymptotes, vertices, and foci. y^2/16 -... (answered by lwsshak3,ewatrrr)

Sketch the hyperbolas. Identify the center, asymptotes, vertices, and foci. (x-3)^2/9 -... (answered by lwsshak3)